The figure shows a metallic cuboid that measures 123 cm by 29 cm by 29 cm.
- Find the maximum number of 7-cm cubes that can be cut from the metallic cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 123 ÷ 7
= 17 r 4
Breath = Height
Number of cubes along the breadth or height
= 29 ÷ 7
= 4 r 1
Maximum number of 7 cm cubes
= 17 x 4 x 4
= 272
(b)
Area of the 2 squares
= 2 x 29 x 29
= 1682 cm
2 Area of the top and bottom bases
= 2 x 123 x 29
= 7134 cm
2 Area of 1 L-shaped side
= 123 x 1 + (29 - 1) x 4
= 123 + 112
= 235 cm
2Area of 2 L-shaped sides
= 2 x 235
= 470 cm
2 Total surface area
= 7134 + 1682 + 470
= 9286 cm
2 Answer(s): (a) 272; (b) 9286 cm
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